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This paper introduces a discrete relaxation for the class of combinatorialoptimization problems which can be described by a set partitioning formulationunder packing constraints. We present two combinatorial relaxations based oncomputing maximum weighted matchings in suitable graphs. Besides providing dualbounds, the relaxations are also used on a variable reduction technique and amatheuristic. We show how that general method can be tailored to sampleapplications, and also perform a successful computational evaluation withbenchmark instances of a problem in maritime logistics.

The matching relaxation for a class of generalized set partitioning problems